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Yes you can (unfortunately). Read here:

I would like to have old classic GB hardware but it seems you can pick any colors and swap as much as you want to ( as long as you have 4 c on screen). So basically you could do any kind of palette-rotating effects. I will personally stick with classic 4 grayscales.

Correct, You can switch your colors as much as you would like, but only 4 colors can be displayed on screen at any one time!

@SetTheBet as for what you are saying, you are more the welcome to stick to the old classic GB hardware :)